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Inhaled hyperpolarized helium-3 (3He) gas is a new magnetic resonance (MR) contrast agent that is being used to study lung functionality. To evaluate the total lung ventilation from the hyperpolarized 3He MR images, it is necessary to segment the lung cavities. This is difficult to accomplish using only the hyperpolarized 3He MR images, so traditional proton (1H) MR images are frequently obtained concurrent with the hyperpolarized 3He MR examination. Segmentation of the lung cavities from traditional proton (1H) MRI is a necessary first step in the analysis of hyperpolarized 3He MR images. In this paper, we develop an active contour model that provides a smooth boundary and accurately captures the high curvature features of the lung cavities from the 1H MR images. This segmentation method is the first parametric active contour model that facilitates straightforward merging of multiple contours. The proposed method of merging computes an external force field that is based on the solution of partial differential equations with boundary condition defined by the initial positions of the evolving contours. A theoretical connection with fluid flow in porous media and the proposed force field is established. Then by using the properties of fluid flow we prove that the proposed method indeed achieves merging and the contours stop at the object boundary as well. Experimental results involving merging in synthetic images are provided. The segmentation technique has been employed in lung 1H MR imaging for segmenting the total lung air space. This technology plays a key role in computing the functional air space from MR images that use hyperpolarized 3He gas as a contrast agent.